THERMAL SCIENCE
International Scientific Journal
A NOVEL SERIES METHOD FOR FRACTIONAL DIFFUSION EQUATION WITHIN CAPUTO FRACTIONAL DERIVATIVE
ABSTRACT
In this paper, we suggest the series expansion method for finding the series solution for the time-fractional diffusion equation involving Caputo fractional derivative.
KEYWORDS
PAPER SUBMITTED: 2016-01-17
PAPER REVISED: 2016-02-23
PAPER ACCEPTED: 2016-03-26
PUBLISHED ONLINE: 2016-09-24
THERMAL SCIENCE YEAR
2016, VOLUME
20, ISSUE
Supplement 3, PAGES [S695 - S699]
- Yang, X. J., et al., Local Fractional Integral Transforms and Their Applications, Academic Press, New York, USA, 2015
- Kilbas, A. A., et al., Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, 2006
- Podlubny, I., Fractional Differential Equations, Academic Press, London, New York, USA, 1999
- Sabatier, J., et al., Advances in Fractional Calculus, Springer, New York, USA, 2007
- Ortigueira, M. D., Fractional Calculus for Scientists and Engineers, Springer, New York, USA, 2011
- Diethelm, K., The Analysis of Fractional Differential Equations: An Application-oriented Exposition Using Differential Operators of Caputo Type, Springer, New York, USA, 2010
- Chen, W., et al., Anomalous Diffusion Modeling by Fractal and Fractional Derivatives, Computers & Mathematics with Applications, 59 (2010), 5, pp. 1754-1758
- Khader, M. M., On the Numerical Solutions for the Fractional Diffusion Equation, Communications in Nonlinear Science and Numerical Simulation, 16 (2011), 6, pp. 2535-2542
- Li, X., et al., A Space-Time Spectral Method for the Time Fractional Diffusion Equation, SIAM Journal on Numerical Analysis, 47 (2009), 3, pp. 2108-2131
- Liu, F., et al., A Fractional-Order Implicit Difference Approximation for the Space-Time Fractional Diffusion Equation, ANZIAM Journal, 47 (2006), June, pp. 48-68
- Dehghan, M., et al., Legendre Spectral Element Method for Solving Time Fractional Modified Anomalous Sub-Diffusion Equation, Applied Mathematical Modelling, 40 (2016), 5-6, pp. 3635-3654
- Yang, X. J., et al., Local Fractional Homotopy Perturbation Method for Solving Fractal Partial Differential Equations Arising in Mathematical Physics, Romanian Reports in Physics, 67 (2015), 3, pp. 752-761
- Yang, X. J., et al., A New Numerical Technique for Solving the Local Fractional Diffusion Equation: Two-Dimensional Extended Differential Transform Approach, Applied Mathematics and Computation, 274 (2016), Feb., pp. 143-151
- Yang, X. J., et al., Local Fractional Similarity Solution for the Diffusion Equation Defined on Cantor Sets, Applied Mathematical Letters, 47 (2015), Sep., pp. 54-60
- Yan, S. P., Local Fractional Laplace Series Expansion Method for Diffusion Equation Arising in Fractal Heat Transfer, Thermal Science, 19 (2015), Suppl. 1, pp. S131-S135
- Yang, A. M., et al., Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets, Abstract Applied Analysis, 2013 (2013), ID 351057
- Zhao, Y., et al., Approximation Solutions for Local Fractional Schroedinger Equation in the One- Dimensional Cantorian System, Advances in Mathematical Physics, 2013 (2013), ID 291386
- Li, Z. B., et al, Fractional Series Expansion Method for Fractional Differential Equations, International Journal of Numerical Methods for Heat & Fluid Flow, 25 (2015), 7, pp. 1525-1530
